The development of the symbolic inverse of a manipulator Jacobian and its use in controlling the manipulator is discussed. The ease of symbolically inverting a matrix is directly related to the simplicity of the expressions in the matrix. Therefore, a general method for obtaining a simplified form of the Jacobian of a manipulator in any of the intermediate link frames is developed and presented using an example. Also, a general method is presented for the verification of a manipulator Jacobian using the forward kinematics. A hand-waving discussion of the inversion of the Kraft slave Jacobian using symbolic manipulation software is given and the final form of the inverse is presented. An approximate solution to the inverse Jacobian problem for the Kraft slave using symbolic inverses is presented. This solution is used in dealing with the only reachable singularity of the Kraft slave. Finally, a teleoperational control system using the inverse Jacobian to calculate the inverse kinematics is discussed.
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